Consider a universe (not ours!) in which spacetime is flat and infinite in size and is populated throughout by stars that cluster into galaxies like our own and our neighbors, with interstellar and intergalactic distances similar to those in our neighborhood. Assume that the galaxies are not moving apart—there is no universal expansion. Using the collisionless Boltzmann equation for photons, show that Earth’s temperature in this universe would be about the same as the surface temperatures of the universe’s hotter stars, ∼10,000 K, so we would all be fried. This is Olbers’ Paradox. What features of our universe protect us from this fate?

Motivated by this model universe, describe a design for a furnace that relies on sunlight for its heat and achieves a temperature nearly equal to that of the Sun’s surface, 5,800 K.